X Likes Cars

X likes to buy and sell cars. For two weeks he bought 5 cars every 12 hours. Then, on June 2nd, he decided to start selling. Every day he would sell 6 cars, then buy 2. But every third day, he would sell 5 cars, and buy 3. X decided that he'll shut down his business when he has no more cars. At this rate, what day will X shut down his business?

Answer

July 12th, 41 days after he started selling.

5 cars every 12 hours = 10 cars per day = 140 cars bought in the two weeks. This is the starting point.

Every two out of three days, he nets 4 cars sold (2 bought - 6 sold). The third day, he nets 2 cars sold (3 bought - 5 sold). This means that he nets 4 + 4 + 2 = 10 cars sold every three days.

Since he needs to sell 140 cars, it will take him 14 3-day cycles to do this. 14 * 3 = 42 days. But on day 41 he sells his 6 cars and runs out. He would normally buy two more later that day, but he is already out.Hide